Compositionality

First published Thu Apr 8, 2004; substantive revision Fri Dec 7, 2012

Anything that deserves to be called a language must contain meaningful
expressions built up from other meaningful expressions. How are their
complexity and meaning related? The traditional view is that the
relationship is fairly tight: the meaning of a complex expression is
fully determined by its structure and the meanings of its
constituents—once we fix what the parts mean and how they are
put together we have no more leeway regarding the meaning of the
whole. This is the principle of compositionality, a fundamental
presupposition of most contemporary work in semantics.

Proponents of compositionality typically emphasize the productivity
and systematicity of our linguistic understanding. We can understand a
large—perhaps infinitely large—collection of complex
expressions the first time we encounter them, and if we understand
some complex expressions we tend to understand others that can be
obtained by recombining their constituents. Compositionality is
supposed to feature in the best explanation of these
phenomena. Opponents of compositionality typically point to cases when
meanings of larger expressions seem to depend on the intentions of the
speaker, on the linguistic environment, or on the setting in which the
utterance takes place without their parts displaying a similar
dependence. They try to respond to the arguments from productivity and
systematicity by insisting that the phenomena are limited, and by
suggesting alternative explanations.

There are many theses called ‘the principle of
compositionality’. The following can serve as a common reference
point:

(C)

The meaning of a complex
expression is determined by its structure and the meanings of its
constituents.

Important variants of the compositionality principle will be presented
below in a form most similar to (C) to facilitate
comparisons.[1]
When formulating more precise versions it is crucial to keep the
pre-theoretical intuitions that led many to accept compositionality
firmly in mind.

The principle of compositionality is normally taken to quantify over
expressions of some particular language L:

(C′)

For every complex
expression e in L, the meaning of e in
L is determined by the structure of e in L
and the meanings of the constituents of e in L.

Questions of structure and constituency are settled by the
syntax of L, while the meanings of simple
expressions are given by the lexical semantics of L.
Compositionality entails (although on many elaborations is not
entailed by) the claim that syntax plus lexical semantics determines
the entire semantics for L.

It makes a big difference whether L is a natural or an
artificial language. Syntactic and semantic questions about a natural
language are settled by and large through empirical investigation;
syntactic and semantic questions about an artificial language are
settled usually by checking what the appropriate stipulations are.
Prima facie, natural languages might turn out not to be
compositional, whereas many artificial languages were designed to meet
such a requirement. (Compositionality is a bonus when it comes to
proof-checking in computer languages, or inductive proofs in logical
calculi.) Unless explicitly noted, talk of compositionality is to be
taken as talk of compositionality of some particular natural language,
or of natural languages in general.

If thought is a kind of language, we can raise the question whether it
is compositional. Thought would not have to be much like
Swahili or the language of set theory for the question to make sense,
but we do need the assumptions that thoughts have meanings (and so,
presumably, are not themselves meanings) and that they have meaningful
constituents. These assumptions follow
from the language of thought hypothesis.
Those who reject this hypothesis may still speak of the
compositionality of thought — but only in an extended sense.

What would such an extended sense be? The key to generalizing
compositionality for non-linguistic representational systems is to
relax the syntactic ideas of constituency and structure. Consider, for
example, the No-Left-Turn sign:

This could be viewed as a complex sign decomposable into meaningful
features — the shape, the color pattern, the arrow, etc. These
features are the analogues of simple expressions: they appear in many
other complex signs and they appear to contribute more or less
uniformly to their meanings.

Once we have an initial grip on what counts as a constituent and how
constituents compose we can legitimately raise the
question whether this system of representations is
compositional.[2]
We may even be able to answer
it.[3]

There is a major debate within the philosophy of mind between
proponents of classical cognitive architecture and proponents
of connectionism.
The debate is typically presented as a debate about compositionality,
but it is not exactly about that. The issue tends to be whether there
are such things as meaningful constituents of thought (perhaps in the
extended sense in which traffic signs can be said to have meaningful
constituents), and if there are, whether these contribute the same
thing (presumably their meaning) to all thoughts in which they
occur. If the answer to the first question is negative, the question
of compositionality does not arise. If the answer to the first
question is positive, the second is independent of
compositionality. (It could be that thought-constituents contribute
always the same thing to a thought of which they are constituents, but
these contributions, even together with the way the constituents are
combined, severely underdetermine the meaning of the thought. And it
could be that thought-constituents contribute different things to
different thoughts — depending on the intentions of the thinker,
or perhaps the surroundings of the thinking — but these variable
contributions, plus the way the constituents are combined, fully
determine the meaning of the thought.) The debate about connectionism
is more closely related to the question whether reverse
compositionality holds (cf. section 1.5.4.)

The principle of compositionality is not committed to a specific
conception of meaning. In fact, it is frequently announced as a
principle that is applicable to whatever a semantic theory might
assign to expressions of a language. Furthermore, although the
reference of an arbitrary expression is definitely not
something one would normally call its ‘meaning’, versions
of the following principle are frequently called ‘the
principle of compositionality’:

(Cref)

For every complex
expression e in L, the reference of e in
L is determined by the structure of e in L
and the references of the constituents of e in
L.

(I use the word ‘reference’ here roughly the way Frege
used his ‘Bedeutung’ after 1892. But it could
also be taken the way Lewis uses ‘extension’. The
differences are significant, but they do not matter for present
purposes.) To avoid confusion, we should call this the principle
of compositionality of reference, and (C) the principle
of compositionality of meaning; when I speak of
compositionality unqualified, what is meant is always the
latter. Since the arguments in favor of compositionality tend
to be based on general considerations about linguistic
understanding—which, I shall suppose amounts to nothing more or
less than understanding what linguistic expressions
mean[4] —
proponents of (Cref) have a choice to make. They can
advocate (Cref) on different grounds or they can claim that
an appropriate theory of the sort that assigns (relative to a variety
of contextually determined
factors[5])
references to expressions can serve as a
theory of meaning.

Formalizations of (C) typically make no assumptions about what
meanings are. This way we achieve generality and stay clear of
dogmatic pronouncements. Still, it is a mistake to abandon all
constraints for that turns compositionality into a vacuous
requirement. It is trivial that we can compositionally
assign something to each expression of a language (for
example, if expressions serve as their own meanings, semantics is
certainly compositional!) but it does not follow that it is trivial
to adequately assign meanings to them.

The point applies to more subtle attempts to trivialize
compositionality as well. Consider a famous result due to Zadrozny (1994).
Given a set S of strings generated from an arbitrary alphabet
via concatenation and a meaning function m which assigns the
members of an arbitrary set M to the members of S,
we can construct a new meaning function μ such that for
all s, t ∈ Sμ(s.t) =
μ(s)(μ(t)) and
μ(s)(s) = m(s). What
this shows is that we can turn an arbitrary meaning function into a
compositional
one,[6]
as long as we replace the old meanings with new ones from which they
are uniformly
recoverable.[7]
But this does not show that it is a trivial matter to devise an
adequate meaning assignment for S. Since synonymy according
to μ does not coincide with synonymy according to
m, we should not accept the claim that μ is as
adequate as m; and since someone ignorant of
m could assign entities to members of S following
μ, we should not accept the claim that the values of the
latter as much deserve to be called meanings as the values of
the former. (For further discussion of Zadrozny's result, see Kazmi
and Pelletier (1998), Westerståhl (1998), Dever (1999).)

Compositionality obviously constrains what meanings might be. But the
constraints apply only to the meanings of complex
expressions — for all (C) tells us the meanings of simple
expressions could be tables and chairs. For let the meanings of
complex expressions be interpreted logical forms, i.e., phrase
structure trees with the meanings of the constituent lexical items
assigned to their terminal nodes. In a fairly straightforward sense
the meanings of lexical items are then parts of the meanings of
complex expressions in which they occur, and so the meanings of
complexes are determined from the relevant tables and chairs together
with their syntactic mode of composition; for similar remarks see
Horwich (1997).

That compositionality does not constrain lexical meaning might appear
paradoxical at first, but the source of paradox is just instability in
how the label ‘compositionality’ is used. Sometimes
compositionality is said to be that feature in a language (or
non-linguistic representational system) which best explains the
productivity and systematicity of our understanding; cf. Fodor (2001):
6. (C) is but one of the features such explanations use — others
include the context-invariance of most lexical meaning, the finiteness
of the lexicon, the relative simplicity of syntax, and probably much
else. These features together put significant constraints on
what lexical meanings might be; cf. the papers collected in Fodor and
Lepore (2002) and Szabó (2004).

Much of what was said above about the need to constrain what counts as
meaning applies to structure as well. Janssen (1986) has a proof that
we can turn any meaning assignment on a recursively enumerable set of
expressions into a compositional one, as long as we can replace the
syntactic operations with different ones. If we insist — as we
should—that any acceptable semantic theory must respect what
syntax tells us about the structure of complex expressions, this
result says nothing about the possibility of providing an adequate
compositional semantics; cf. Westerståhl
(1998).[8]
The moral of the result is that although commitment to
compositionality requires allegiance to no particular sect of
syntacticians, one cannot be oblivious to syntactic evidence in
semantic theorizing.

(C) does not require the kind of tight correspondence between syntax
and semantics we intuitively associate with compositionality. To
illustrate this, consider a view, according to which the meaning of a
declarative sentence s is the set of possible worlds where
s is true. According to such a view, tautologies are
synonymous, even though (since Rudolf presumably has some tautological
beliefs and lacks others) sentences resulting from embedding
tautologies under ‘Rudolf believes that…’ are
not. (I also assume a straightforward semantics for propositional
attitudes without hidden indexicals or tacit quantification.)
Intuitively, this is a violation of compositionality. Still, the
semantics is not in conflict with (C): tautologies might
differ structurally or in the meaning of their constituents, which
could explain how their embedding can yield non-synonymous sentences;
cf. Carnap (1947) and Lewis (1970).

To rule a semantic theory like this one non-compositional, we need to
demand that the meaning of a complex expression be determined by its
immediate structure, and the meanings of its
immediate constituents. (The immediate structure of an
expression is the syntactic mode its immediate constituents are
combined. e is an immediate constituent of e′
iff e is a constituent of e′ and
e′ has no constituent of which e is a
constituent.)

(Clocal)

For every complex
expression e in L, the meaning of e in
L is determined by the immediate structure of e in
L and the meanings of the immediate constituents of
e in L.

Call the strengthened principle local compositionality, and
(C) global compositionality; when unqualified,
‘compositionality’ should be taken as global. The local
principle is more intuitive, and semanticists frequently presuppose
it. In fact, some theorists assume not only (Clocal), but
also that concatenation is uniformly interpreted as functional
application, or perhaps as conjunction; cf. Pietroski (2005, 2012). If
so, we can omit explicit talk of structure and say simply that the
meanings of complex expressions are determined by the meanings of
their immediate constituents. Others insist that the relevant notion
of structure (Clocal) appeals to is the one apparent on the
surface of sentences, and accordingly, our syntax should not postulate
movement or empty elements; cf. Jacobson (2002, 2012). Clearly, appeal
to our ability to understand novel expressions in itself provides no
direct support for such any of these strong claims.

Intuitively, if a language is compositional it cannot contain a pair
of non-synonymous complex expressions with identical structure and
pairwise synonymous constituents. This should follow from the fact
that the same structure and the same meanings of constituents cannot
determine more than one meaning within a language. But to ensure that the inference really holds, we need to rule out a certain reading of (C).

Fine (2007) advocates the following view: ‘Cicero’ and
‘Tully’ are synonyms, but ‘Cicero is Cicero’
and ‘Cicero is Tully’ are not, despite the fact that these
sentences do have the same structure. The meaning-difference arises
from the fact that the former sentence encodes semantic co-reference
but the latter does not. All this is fully compatible with English not
being a counterexample to (Ccoll):

(Ccoll)

For every complex
expression e in L, the meaning of e in
L is determined by the structure of e in
L and the meanings of the constituents of
e in L collectively.

On Fine's view, what the constituents of ‘Cicero is
Cicero’ collectively mean goes beyond what the
constituents of ‘Cicero is Tully’ do. The collective
meaning comprises the individual meanings plus certain
meaning-relations that hold among them. Call the weak principle
(Ccoll) collective compositionality; following
usual practice (C) will be understood as distributive
compositionality.

It is clear that the meanings of complex expressions depend individual
meanings of their parts. Thus, the only chance for (Ccoll)
to be true is if the collective meaning of constituents (whatever that
might be) determines each of the individual meanings of
constituents. This is certainly so on Fine's view: he thinks the
meaning of ‘Cicero is Cicero’ depends on its structure
(this is why it is not synonymous with ‘Is Cicero
Cicero?’), on the individual meanings of its constituents (this
is why it is not synonymous with ‘Cicero is Caesar’),
and in addition on the intended co-reference relation between
the subject and the object, which is an aspect of the collective
meaning of its constituents (this is why it is not synonymous with
‘Cicero is Tully’).

Given the distributive reading, (C) rules out the existence of a pair
of non-synonymous complex expressions with identical structure and
pairwise synonymous constituents within a single language. But (C)
remains silent on the possibility of such pair existing
in distinct languages. But this is an open violation of what
we normally mean by determination.

Here is an illustration from Szabó (2000b). Suppose English is
compositional. Take two of its non-synonymous sentences — say,
‘Elephants are grey’ and ‘Julius Caesar was murdered
on the ides of March’ — and define Crypto-English as the
language with the same expressions, the same syntax and almost the
same semantics as English. The only difference is that if a
sentence is synonymous in English with one of the two designated
sentences, then it is synonymous with the other in Crypto-English. We
assumed English is compositional and hence that there is no pair of
non-synonymous complex expressions in English with identical structure
and pairwise synonymous constituents. Trivially, the same must hold
for Crypto-English as well. But intuitively, Crypto-English is
not compositional. The structure and the meanings of
constituents of the Crypto-English sentence ‘Elephants are
grey’ cannot determine what this sentence means in
Crypto-English — if they did then the structure and the meanings
of constituents of the English sentence ‘Elephants are
grey’ would have to determine what ‘Julius Caesar was
murdered on the ides of March’ means in English.

If we want a better match with our intuitions, we must demand more
from a compositional language than the mere existence of a
function from structures and the meanings of parts to the
meanings of wholes. One possibility would be to put constraints on
this function — we could demand, for example that it be
computable, or perhaps even that the computation be reasonably
quick. But the above example shows that such a strengthening would not
solve the problem: if computing the meanings of complex expressions is
easy in English, it will not be hard in Crypto-English either. We
might instead opt for the following strengthening of (C):

(Ccross)

For every complex
expression e in L, the meaning of e in
L is functionally determined through a single function for
all possible human languages by the structure of e in
L and the meanings of the constituents of e in
L.

Call the strengthened principle cross-linguistic
compositionality, and (C) — when ‘determine’ is
simply read as ‘functionally determine’ and we may have
different functions for different languages — language-bound
compositionality. Note that formal languages that are designed to
satisfy language-bound compositionality may nonetheless violate
cross-linguistic compositionality simply because their syntax or the
meanings of their constituents violate some universal constraint on
human languages. Note also that whatever the epistemic status of other
version of the principle of compositionality might be, cross-linguistic
compositionality is clearly an empirical hypothesis.[9]

When speaking of compositionality unqualified,
I will always mean language-bound compositionality. Again, the
stronger principle is much closer to our pre-theoretic intuitions and
it is often tacitly assumed in practice. But the traditional
considerations in favor of compositionality support the weaker thesis
only.

The fact that natural languages contain indexicals forces us to
distinguish between two notions of meaning. On the one hand,
expressions have a standing meaning fixed by convention and
known to those who are linguistically competent. On the other hand, in
use expressions are associated with occasion meanings which
is discerned by interpreters in part on the basis of contextual
information. The terminology is from Quine (1960). Kaplan (1977) uses
the terms character and content but he makes a
number of substantive assumptions about what these are which I intend
to abstract from. Thus, we should not assume that occasion meanings
are structured entities built from objects, properties, and relations,
or even that the occasion meanings of declarative sentences are always
propositions. Also, we need not assume that standing meanings are
functions from contexts to occasion meanings, or even that they
determine in context what occasion meanings are.

When we speak of meaning, usually we have standing meaning in
mind. But not always — when a contract specifies that within its
main text ‘current edition of building code’ means the
2012 edition of the Florida Building Code, it obviously fixes occasion
meaning. Corresponding to these two notions of meaning, there are two
versions of the principle of compositionality. Since occasion-meaning
is determined, in part, by context (Cocc) must be
relativized to context:[10]

(Cstand)

For every complex
expression e in L, the standing meaning of e in
L is determined by the structure of e in
L and the standing meanings of the constituents of e in
L.

(Cocc)

For every complex expression e in
L and every context c, the occasion meaning of e
in L at c
is determined by the structure of e in
L and the occasion meanings of the constituents of e in
L at c.

Let's call expressions whose occasion meaning sometimes
deviates from their standing meaning context-dependent. The
scope of context-dependent lexical items is a matter of
controversy. On the one extreme, there are semantic
minimalists who think these include only a handful expressions:
the personal and demonstrative pronouns, a few adverbs
(e.g. ‘here’, ‘now’, ‘next’), and
a few adjectives (e.g.‘actual’, ‘present‘,
‘local’); cf. Cappelen and Lepore (2005). On the other
extreme are radical contextualists who think essentially all
lexical items are context-dependent; e.g. Searle (1980). As usual,
most theorists are somewhere in the middle — taking heat from
both sides that their view is untenable.

Radical contextualism is sometimes seen as a challenge to
compositionality, more precisely, to (Cocc); cf. Cohen
(1986), Lahav (1989), Fodor(2001a). It shouldn't be. An effective
argument from context-dependence against (Cocc) would need
to show that there is at least one complex expression in L
whose occasion meaning varies with context, while the occasion
meanings of its constituents all remain the same. The usual
considerations against compositionality typically omit the second
part. Take for example Searle's observation that “[t]he
sort of thing that constitutes cutting the grass is quite different
from e.g., the sort of thing that constitutes cutting a cake;”
cf. Searle (1980): 222. What follows from this? Maybe we should
conclude that in a typical context, the occasion meaning of ‘cut
the grass’ differs from the occasion meaning of ‘cut the
cake’. As long as the occasion meaning of ‘cut’ is
appropriately sensitive to the its linguistic environment, this is
fully compatible with (Cocc).

Of course, we should not insist that the occasion meaning of
‘cut’ depends on nothing but its standing meaning and the
linguistic environment in which it occurs. As Searle himself
emphasized, ‘cut the grass’ can pick out one sort of thing
if we are using it in a context of selling strips of grass turf and
another it we are using in a context of selling lawn mowers. Arguably,
this shows that the occasion meaning of ‘cut’ depends on
extra-linguistic factors as well. No matter: this too is fully
compatible with (Cocc). Compositionality demands nothing
more than that all context-dependence be accounted for via
context-dependence in the lexicon and it takes no stance of how much
and what kind of lexical context-dependence there might be;
cf. Szabó (2010), Lasersohn (2012), and Recanati
(2012).[11]

We have distinguished several interpretations for the seemingly simple
claim that a certain language is compositional and we picked a fairly
natural one. Thus, we proposed to read (C) as being about meaning (as
opposed to reference or some other value one might assign to
expressions), that it postulates functional determination of meaning
within a particular language (as opposed to across a class of
languages), and that the determinants of the meaning of a complex
expression are its entire structure (as opposed to just its immediate
structure) and the meanings of its constituents individually (as
opposed to collectively). We saw that (C) remains ambiguous even after
these clarifications, for there are at least two kinds of meaning it
could be about (standing meaning and occasion meaning). If it is
intended to be about occasion meaning, it must involve a suppressed
quantification over contexts (just as it contains a suppressed
quantification over languages).

There are a number of principles worth mentioning that are often
discussed along with (and are occasionally confused with) the
principle of compositionality. It is useful to see which, if any of
them is equivalent to (C).

Consider first the often cited principle that says that substitution
of synonyms is always meaning-preserving. As stated, the principle
requires clarification. For one thing, not every case of replacement
counts as substitution: the expression we replace with its synonym
within a larger expression must be a constituent of the larger
expression. Otherwise, as Geach pointed out, the synonymy of
‘Plato was bald’ with ‘Baldness was an attribute of
Plato’ would guarantee the synonymy of ‘The philosopher
whose most eminent pupil was Plato was bald’ and ‘The
philosopher whose most eminent pupil was baldness was an attribute of
Plato’; cf. Geach (1965):110.

In addition, we need to separate two issues: whether substitution of
synonyms can turn a meaningful expression into a meaningless one, and
whether it can turn a meaningful expression into an expression with a
different meaning. The principle that rules out the former possibility
was first proposed by Husserl (1913): 318, and it is usually stated in
terms of the notion of a semantic category. Two expressions
belong to the same semantic category just in case they are
intersubstitutable within any meaningful expression salva
significatione (without loss of meaningfulness). According to
Husserl's principle:

(H)

Synonyms belong in the same semantic category.

(H) is a rather controversial — intuitively, there are many
synonyms that are not everywhere intersubstitutable. For example,
‘likely’ and ‘probable’ mean pretty much the
same even though ‘Jacques is likely to leave’ is
meaningful while ‘Jacques is probable to leave’ is
arguably not; cf. Gazdar (1985):
32.[12]
And — more controversially — there might be synonyms that
are almost nowhere intersubstitutable: ‘quick’ and
‘quickly’ are good candidates.

The principle that rules out the possibility that substitution of
synonyms could turn a meaningful expression into one with a different
meaning comes in two versions:

(Ssingular)

If two meaningful
expressions differ only in that one is the result of substituting a
synonym for a constituent within the other then the two expressions
are synonyms.

(Splural)

If two meaningful
expressions differ only in that one is the result of substituting some
synonyms for some constituents within the other then the two
expressions are synonyms.

Assuming the language under discussion has a grammar that requires
that each constituent of a meaningful complex expression be itself
meaningful (Splural) is stronger than (C) — it is
equivalent to local, distributive, language bound
compositionality of meaning. Assuming in addition that the language
satisfies (H), (Ssingular) is equivalent to
(Splural); cf. Hodges (2001) Theorem 4.

Sometimes the claim that L is compositional is presented
directly as a claim about the relationship between its syntax and
semantics. The following thesis is often called the rule-to-rule
principle:

(RR)

To every syntactic rule
corresponds a
semantic rule that assigns meanings to the output of the syntactic rule
on the basis of the meanings of its inputs.

How strong a claim (RR) is depends on what counts as a rule. If an
arbitrary function deserves that name, the rule-to-rule principle is
stronger than (C): it is equivalent to local, distributive, language
bound compositionality of meaning. But if we insist — quite
plausibly — that a semantic rule must be computable (or perhaps
easily computable) the rule-to-rule principle is stronger than
that. And if we assume that rules must have some sort of psychological
reality, (RR) says something completely different from (C).

Ordinarily when we say that something determines something else we
think of the former as being causally or explanatorily prior to the
latter. Although the principle of compositionality is usually not
understood in this way, sometimes philosophers read it as a principle
that asserts the priority of word meaning over sentence meaning, or
more generally, the priority of the meanings of lexical items over the
meanings of complex expressions:

(P)

Complex expressions have
their meanings in virtue of their structure and the meanings of
their constituents.

(P) is often thought to be in tension with the idea that each
expression has the meaning it does in virtue of the way it is used
within some linguistic community. The conflict is supposed to arise
because (i) the use of an expression is exhausted by its employment in
speech acts, and (ii) it is sentences, not words, that can be employed
to make speech acts. Against this, it can be argued that
referring is among the speech acts speakers routinely perform
and that this speech act is done with words, not sentences. One might
try to replace (i) with a stronger claim, for example, that the use of
an expression is exhausted by its employment in asserting,
asking, commanding, and a few of other speech acts
not including referring. But even if true the stronger claim
may not save the argument against (P) because, at least prima
facie, we can make assertions uttering isolated words;
cf. Stainton (2006). Davis (2003) develops a detailed theory of
meaning that combines (P) with a version of the use theory of
meaning.

To say that there is no easy argument against (P) is a far cry from
saying that it must be true. It is important to keep in mind that (P)
is significantly stronger than (C) and that the usual arguments in
favor of compositionality cannot by themselves justify it.

In section 60 of the Foundations of Arithmetic Frege famously
declares that only within a complete sentence do words have
meaning. This has come to be referred to in the literature as
Frege's context principle. Frege writes that “it
is enough if the sentence as whole has meaning; thereby also its parts
obtain their
meanings”.[13]
On the face of it, this asserts that words have their meanings in
virtue of the meaning of sentences in which they occur as
constituents. This is incompatible with (P), but not with (C). Even if
words are meaningful only because they occur as constituents within
sentences, there could still be a function (perhaps even a single
function across all possible human languages) that maps the structure
of a sentence and the meanings of its constituent words to the meaning
of that sentence.

There is an alternative way to construe Frege's principle, a way
that makes it a determination claim, not a primacy claim. To state it
in a form that matches the generality of (C) we should drop the talk
of words and sentences, and talk instead about complex expressions and
their constituents:

(Fall)

The meaning of an expression
is determined by the meanings of all complex expressions in
which it occurs as a constituent.

Like the principle of compositionality, (Fall) can be
interpreted as a claim about reference or meaning, locally or
globally, collectively or distributively, in a language-bound manner
or cross-linguistically. Compositionality is about bottom-up
meaning-determination, while the context principle about top-down
meaning-determination. As long as it is not understood as a causal or
explanatory relation determination can be symmetric, so any version of
(C) is compatible with the corresponding version of
(Fall).

There is a strengthening of (Fall), according to which the
meaning of an expression is determined not only by the meanings of
all expressions in which it occurs as a constituent, but by
the meaning of any one of these expressions:

(Fany)

The meaning of an expression
is determined by the meaning of any complex expression
in which it occurs as a constituent.

(Fany) is an immediate consequence of the converse of
(C) — sometimes called reverse compositionality —
according to which the meaning of a complex expression determines the
structure of the expression and the meanings of its
constituents. (Fodor (1998b), Fodor and Lepore (2001), Pagin (2003)
advocate reverse compositionality; Patterson (2005), Robbins (2005),
Johnson (2006) are among its opponents. The debate is complex, in part
because at least some proponents of reverse compositionality advocate
it only for the language of thought; cf. Fodor (2001).)

(Fany) is a very strong thesis and most standard semantic
theories are incompatible with it. Take, for example, a simple
Carnapian semantics that assigns to each sentence the set of possible
worlds where it is true. Suppose we are considering a language that
contains the standard logical operators, and so any sentence is a
constituent of a necessarily true sentence. Since the meaning of a
necessary truth is the set of all possible worlds, this set would have
to determine the meanings of all sentences in the language, which is
absurd.

A principle of intermediate strength between (Fall) and
(Fany) is (Fcof):

(Fcofinal)

The meaning of an expression
is determined by the meanings of all expressions
within any cofinal set of expressions.

(A cofinal set of expressions is a set such that any expression occurs
as a constituent in at least one member of the set. Except for very
odd languages, the set of all expressions within the language in which
some given expression occurs as a constituent is one of many cofinal
sets of expressions, so (Fall) follows from
(Fcof) but not the other way around. That (Fcof)
follows from (Fany) but not the other way around is
trivial.)

One interesting feature of (Fcofinal) is that it appears to
be in conflict with a Quine's thesis of the indeterminacy of
translation (taken as a thesis that implies the indeterminacy of
meaning). Assume that the set of all observation sentences is cofinal
within a reasonably large fragment of a natural language and that the
meaning of an observation sentence is identical to its stimulus
meaning — (Fcofinal) ensures then that the meanings
of all the words are determined within our fragment. Recently there
has been an attempt to show that (Fcofinal) follows from
less controversial claims, and perhaps even from claims that Quine
himself was committed to; cf. Werning (2004). The heart of
Werning's argument is the Extension Theorem;
cf. Theorem 14 in Hodges (2001). The theorem states that a meaning
assignment to a cofinal set of expressions that satisfies (H) and
(Ssingular) has a unique extension to a meaning assignment
to all expressions that satisfies (H), (Ssingular) as well
as its converse. (There is a generalized result mentioned in Hodges
(2012): 257.) The extra assumptions needed to get from the Extension
Theorem to a denial of indeterminacy remain questionable; cf. Leitgeb
(2005).

The claim that L is compositional is often taken to mean that
the meaning of an arbitrary complex expression in L is built
up from the meanings of its constituents in L — call this
the building principle for L. This is a fairly
strong claim, at least if we take the building metaphor seriously. For
then the meanings of complex expressions must themselves be complex
entities whose structure mirrors that of the sentence; cf. Frege
(1892), Frege (1919). This presumably entails but is not entailed by
local distributive cross-linguistic compositionality of meaning.

Montague (1970) suggested a perspicuous way to capture the principle
of compositionality formally. The key idea is that compositionality
requires the existence of a homomorphism between the
expressions of a language and the meanings of those expressions.

Let us think of the expressions of a language as a set upon which a
number of operations (syntactic rules) are defined. Let us require
that syntactic rules always apply to a fixed number of expressions and
yield a single expression, and let us allow that syntactic rules be
undefined for certain expressions. So, a syntactic algebra is
a partial algebra E
= 〈E,
(Fγ)γ∈Γ〉,
where E is the set of (simple and complex) expressions and
every Fγ is a partial syntactic operation on
E with a fixed arity. The syntactic algebra is interpreted
through a meaning-assignment m, a function from E to
M, the set of available meanings for the expressions of
E.

Consider now F, a k-ary syntactic operation on
E. m is F-compositional just in case there
is a k-ary partial function G on M such
that whenever
F(e1,…,ek) is
defined,

m(F(e1,…,ek))
=
G(m(e1),…,m(ek)).

(In English: there is a partial function from the meanings of
e1,…,ek to the meaning
of the expression built from
e1,…,ek through an
application of the syntactic rule F.)

Finally, we can say that m is compositional
simpliciter just in case m is
F-compositional for each syntactic operation in
E. Whenever m is compositional, it induces
the semantic algebra M = 〈M,
(Gγ)γ∈Γ〉
on M, and it is a homomorphism between E
and M; cf. Westerståhl (1998). (For details,
variants, and formal results, see Janssen (1986), (1997), Hodges
(2001), and Pagin and Westerståhl (2010a). For generalizations
that cover languages with various sorts of context-dependence, see
Pagin (2005), Pagin and Pelletier (2007) and Westerståhl
(2012).)

Since there are no restrictions on what m assigns to members
of E, the formal statement captures both compositionality of
reference and compositionality of meaning. As stated, the principle
captures local distributive language-bound compositionality: it requires that each
application of each syntactic rule within a language be matched by an
application of an appropriate semantic function. To capture
cross-linguistic compositionality is easy: all we need to say is that
the expressions within E are the expressions of all possible
human languages. (Of course, if we allow the syntactic algebra to
contain expressions of different languages, we may want to insist that
syntactic operations map expressions of a language onto complex
expressions of the same language and that they remain undefined for
cases when their argument positions are filled by expressions from
different languages.[14])

To capture global compositionality is more complicated. Here is an
attempt. Let us say that the expressions e and
e′ are local equivalents just in case they are
the results of applying the same syntactic operation to lists of
expressions such that corresponding members of the lists are
synonymous. (More formally: for some natural number k there
is a k-ary F in E, and there are
some expressions
e1,…,ek,
e1′,…,ek′
in E, such that e =
F(e1,…,ek),
e′ =
F(e1′,…,ek′),
and for every 1≤ i ≤ k,
m(ei) =
m(ei′).) It is clear that
m is locally compositional just in case locally equivalent
pairs of expressions are all synonyms. Let us say that the expressions
e and e′ are global equivalents just
in case they are the results of applying the same syntactic operation
to lists of expressions such that corresponding members of the lists
are either (i) simple and synonymous or (ii) complex and globally
equivalent. (Here is the recursive definition more formally. Let us
say that the expressions e and e′ are
1-global equivalents just in case they are synonymous simple
expressions. Let us say that the expressions e and
e′ are n-global equivalents just in case for
some natural number k there is a k-ary F in
E, and there are some expressions
e1,…,ek,
e1′,…,ek′
in E, such that e =
F(e1,…,ek),
e′ =
F(e1′,…,ek′),
and for every 1 ≤ i ≤ k there is a 1 ≤
j < n such that ei and
ei′ are j-global equivalents.
Finally, let us say that the expressions e and
e′ are global equivalents just in case for
some natural number n they are n-global
equivalents.)[15]
I suggest that m is globally compositional just in case
globally equivalent pairs of expressions are all synonyms.

Collective compositionality is a further weakening of global
compositionality. It could be formalized using the same trick. Thus,
we can say that m is collectively compositional just in case
collectively equivalent pairs of expressions are all synonyms, where
we define collective equivalence exactly like global equivalence with
one difference. In the recursive step we demand not only
that ei and
ei′ be j-collective equivalents but
also that the very same semantic relations should hold
among e1,…,ek
and among e1′,…,ek′.
Thus, we leave space for the possibility that ‘Cicero is
Cicero’ is not collectively equivalent to ‘Cicero is
Tully’, even though they have the same structure and their
proper constituents are all collectively equivalent; see section 1.4.

The simplest argument for compositionality is that it is supported by
intuitions many claim to have about meaning and structure. Although
there are interesting putative counterexamples (see section 4.2.) they
probably can be explained away through modest revisions of our
syntactic and/or semantic theories. This defense is reasonable but
much too modest. For even if it succeeds in convincing some who aren't
already convinced, it leaves us all in the dark why
compositionality is true. Defenders of compositionality should do
better than this.

The argument most often used to support compositionality is based on
productivity. It goes back (at least) to Frege, who claimed that
“the possibility of our understanding sentences which we have
never heard before rests evidently on this, that we can construct the
sense of a sentence out of parts that correspond to words.”
(Frege 1914?: 79) The argument is an inference to the best
explanation, which can be expanded and rephrased without assuming that
meanings are Fregean
senses.[16]

Argument from productivity: Since competent speakers can
understand a complex expression e they never encountered
before, it must be that they (perhaps tacitly) know something on the
basis of which they can figure out, without any additional
information, what e means. If this is so, something they
already know must determine what e means. And this knowledge
cannot plausibly be anything but knowledge of the structure of
e and knowledge of the individual meanings of the simple constituents of
e.

To bolster the claim that we do, in fact, understand complex
expressions we never heard before, philosophers often appeal to
unboundedness: although we are finite beings we have the
capacity to understand each of an infinitely large set of complex
expressions. Although there are dissenters — e.g., Ziff
(1974) — the claim that natural languages contain infinitely many
complex expressions is
plausible.[17]
But it is equally plausible that nobody who reads this entry the
first time has ever encountered this very sentence before, and
consequently, the detour through cardinality considerations seems
superfluous. Occasionally, the fact that natural languages are
learnable is also used to argue for compositionality. This is
not an independent argument: the reason it is remarkable that we can
learn a natural language is that once we have learnt it our
understanding is productive. If we could not understand expressions we
never encountered before, without detailed empirical study we could
not rule out the hypothesis that we learned the language in question
by rote.

The first thing to point out about the argument from productivity is
that it is an argument in favor of (C) — global distributive
language-bound compositionality of meaning. As it stands, it provides
no reason for believing anything this principle does not entail; in
particular it cannot establish (Cref), (Clocal),
or (Ccross).

The argument can be
criticized on the ground that considerations of this sort simply
cannot establish a universal claim. Suppose someone suggests that the
complex expression e is a counterexample to (C). The fact
that we tend to understand all sorts of complex expressions we never
heard before does not mean that we would understand e on the
first encounter. But suppose we would. Still, even if in
general we tend to understand complex expressions we never heard
before in virtue of our knowledge of their structure and the meanings
of their simple constituents, we might understand e in some
other way. General considerations of productivity cannot rule
out isolated exceptions to compositionality. (Isolated
putative exceptions are often declared to be idioms—expressions
whose syntactic complexity is only apparent. But unless we are
given clear non-semantic grounds for singling out idioms, the move is
question-begging. Such criteria have been proposed, but they tend to
be rather controversial; cf. Nunberg, Sag and Wasow (1994).)

If we lower our sights and seek to prove nothing more than the claim
that natural languages by and large obey global distributive
language-bound compositionality of meaning, the argument from
productivity is reasonably strong.

Another argument in favor of compositionality is based on
systematicity, the fact that there are definite and
predictable patterns among the sentences we understand. For example,
anyone who understands ‘The rug is under the chair’ can
understand ‘The chair is under the rug’ and vice
versa. This is also an inference to the best explanation, and can
be summarized as follows:

Argument from systematicity: Anyone who understands a complex
expression e and e′ built up through the
syntactic operation F from constituents
e1,…,en and
e1′,…,en′
respectively, can also understand any other meaningful complex
expression e″ built up through F from
expressions among
e1,…,en,
e1′,…,en′. So,
it must be that anyone who knows what e and
e′mean is in the position to figure out, without any
additional information, what e″ means. If this is so,
the meaning of e and e′ must jointly
determine the meaning of e″. But the only plausible way
this could be true is if the meaning of e determines
F and the meanings of
e1,…,en, the meaning of
e′ determines F and the meanings of
e1′,…,en′,
and F and the meanings of
e1,…,en ,
e1′,…,en′
determine the meaning of e″.

Although the arguments from productivity and systematicity are usually
alluded to in the same breath, they are very different
considerations. Unlike the main premise of the former, the main
premise of the latter is anything but obvious. Particular instances
are plausible enough: it seems reasonable that anyone who can
understand ‘The dog is asleep’ and ‘The cat is
awake’ can also understand ‘The dog is awake’ and
‘The cat is asleep’, and that anyone who can understand
‘black dog’ and ‘white cat’ can also
understand ‘black cat’ and ‘white dog’. But do
all who understand ‘within an hour’ and ‘without a
watch’ also understand ‘within a watch’ and
‘without an hour’? And do all who understand
‘halfway closed’ and ‘firmly believed’ also
understand ‘halfway believed’ and ‘firmly
closed’? As Johnson (2004) argues, the claim that natural
languages are systematic presupposes a natural non-overlapping
linguistic categorization of all the expressions. The existence of
such a categorization is a bold empirical hypothesis.

Fodor (1998b) does offer an empirical argument in favor of
systematicity. The idea is that if complex expressions could be
understood without understanding their constituents then it is unclear
how exposure to a corpus made up almost entirely of complex
expressions could suffice to learn the meanings of lexical items. But,
as a matter of empirical fact, children learn the meanings of words by
encountering them almost exclusively within other
expressions. However, as Robbins (2005) points out, this observation
can at best lead one to conclude that understanding a suitably
large set of complex expressions in which a given expression
occurs as a constituent suffices for understanding the constituent
itself. It does not show that understanding any complex
expression suffices for understanding its constituents.

The arguments from productivity and systematicity differ in what
they aim to prove. First, the argument from systematicity proves
something weaker than (any version of) compositionality. If we run the
argument for the pair of sentences ‘The dog is asleep’ and
‘The cat is awake’ we can conclude that the meanings of
‘the dog’, ‘the cat’, ‘is asleep’
and ‘is awake’ plus predication determine the meaning of
‘The dog is awake’. It does not follow that the
meanings of ‘the dog’ and ‘is awake’ plus
predication do that. Second, if this problem can be fixed somehow, the
argument from systematicity proves not only global, but
local compositionality: it tells us that the meanings of
immediate constituents and immediate structure fix the meanings of
complex expressions. Finally, if successful, the argument from
systematicity proves not only a version of the compositionality
principle, but also reverse compositionality. We are invited to conclude
that the meaning of an arbitrary complex expression determines its
immediate structure and the meanings of its immediate constituents;
cf. section 1.5.4, Fodor and Lepore (2001): 59, Pagin (2003): 292.

As with the argument from productivity, the argument from
systematicity is unable to screen out isolated counterexamples. Still,
it is a reasonably strong consideration in favor of the claim that natural
languages by and large obey language-bound distributive local
compositionality of meaning and its reverse.

By far the most popular reason for believing in compositionality is
that it works. Linguists have adopted various versions of the
principle as a working hypothesis and developed semantic theories on
their basis. These theories have provided intuitively satisfactory
explanations for certain data, such as the validity or invalidity of
certain inferences or for various sorts of contrasts between certain
minimal pairs. Moreover, whenever it was suggested that certain
phenomena require abandonment of the principle, it was subsequently
shown that this is not so: reasonably elegant and comparatively
natural compositional theories were just around the corner;
cf. section 4.2.

Despite its popularity, this is not a very good reason to believe in
compositionality. The fact that compositional semantic theories can
explain certain things does not show that they explain those
things because they are compositional. Do we have reason to
think that without assuming compositionality we would not be able to
explain the same things? It seems to me that we have no such reason:
semanticists have focused on whether they can hold on to
compositionality while providing satisfactory explanations, not on
whether they have to embrace compositionality in order to
provide satisfactory explanations. We are not entitled to assume that
adopting compositionality as a working hypothesis has in any way
contributed to explanatory success in semantics.

A much more promising methodological argument for compositionality
goes as follows. The fact that we are able to communicate in real time
makes it overwhelmingly likely that the computational complexity of
the interpretation algorithm we employ is relatively low. In fact, it
seems reasonable to think that semantic theories with minimal
complexity are, other things being equal, preferable. And there are
certain results that show that, under certain conditions, semantics
theories that conform to a certain strengthening of (C) will be
minimally complex; cf. Pagin (2012). Alas, the conditions in question
tend to be unrealistic for natural languages. Nonetheless, we can
think of them as idealizations, which makes adoption of
compositionality as a working hypothesis still a reasonable one.

Considerations regarding productivity and systematicity are
powerful. It does seem to many that the explanation of these phenomena
that presupposes compositionality is not only the best, but also the
only one imaginable. So, before I survey some of the putative
counterexamples to compositionality from the semantic literature, to
bolster the imagination I will discuss a simple non-linguistic case
where our understanding is productive and systematic despite apparent
lack of compositionality in the system of representations.

Consider the Algebraic notation for
chess.[18]
Here are the basics. The rows of the chessboard are represented by
the numerals 1, 2, … , 8; the
columns are represented by the lower case letters a,
b, … , h. The squares are identified by
column and row; for example b5 is at the intersection of the
second column and the fifth row. Upper case letters represent the
pieces: K stands for king, Q for queen, R
for rook, B for bishop, and N for knight. Moves are
typically represented by a triplet consisting of an upper case letter
standing for the piece that makes the move and a sign standing for the
square where the piece moves. There are five exceptions to this: (i)
moves made by pawns lack the upper case letter from the beginning,
(ii) when more than one piece of the same type could reach the same
square, the sign for the square of departure is placed immediately in
front of the sign for the square of arrival, (iii) when a move results
in a capture an x is placed immediately in front of the sign
for the square of arrival, (iv) the symbol 0-0 represents
castling on the king's side, (v) the symbol 0-0-0 represents
castling on the queen's side. + stands for check, and ++ for
mate. The rest of the notation serves to make commentaries about the
moves and is inessential for understanding it.

Someone who understands the Algebraic notation must be able to follow
descriptions of particular chess games in it and someone who can do
that must be able to tell which move is represented by
particular lines within such a description. Nonetheless, it is clear
that when someone sees the line Bb5 in the middle of such a
description, knowing what B, b, and 5 mean
will not be enough to figure out what this move is supposed to be. It
must be a move to b5 made by a bishop, but we don't know
which bishop (not even whether it is white or black) and we don't know
which square it is coming from. All this can be determined by
following the description of the game from the beginning, assuming
that one knows what the initial configurations of figures are on the
chessboard, that white moves first, and that afterwards black and
white move one after the other. But staring at Bb5 itself
will not help.

The first moral of the example is that we can have productive and
systematic understanding of representations even if we do not
understand complex representations merely by understanding
their simple components and the way those components are combined. The
reason this could happen is that all who understand the system know
certain things (e.g., the initial configuration of pieces and the
order of moves) from which they can figure out the missing information
(e.g., which figure is moving and from where).

The second moral is that — given certain assumptions about
meaning in chess notation—we can have productive and systematic
understanding of representations even if the system itself is not
compositional. The assumptions in question are that (i) the
description I gave in the first paragraph of this section fully
determines what the simple expressions of chess notation mean and also
how they can be combined to form complex expressions, and that (ii)
the meaning of a line within a chess notation determines a move. One
can reject (i) and argue, for example, that the meaning of B
in Bb5 contains an indexical component and within the context
of a description, it picks out a particular bishop moving from a
particular square. One can also reject (ii) and argue, for example,
that the meaning of Bb5 is nothing more than the meaning of
‘some bishop moves from somewhere to square
b5’ — utterances of Bb5 might carry
extra information but that is of no concern for the semantics of the
notation. Both moves would save compositionality at a price. The first
complicates considerably what we have to say about lexical meanings;
the second widens the gap between meanings of expressions and meanings
of their utterances. Whether saving compositionality is worth either
of these costs (or whether there is some other story to be told about
our understanding of the Algebraic notation) is by no means clear. For
all we know, Algebraic notation might be non-compositional.

We now discuss briefly four famous putative counterexamples to the
compositionality of English from the semantic literature. The list is
not supposed to be representative but by no means exhaustive. (For a
more systematic survey of how compositionality problems are typically
solved in formal semantics, see Zimmerman (2012).) In each case, we
also indicate what reasonable responses to the challenges might look
like.

Putative counterexamples to (C) are always complex expressions whose
meaning appears to depend not only on the meanings of their
constituents and on their structure but on some third factor
as well. Sometimes this third factor is linguistic context: what a
complex expression means seems to depend in part on how it is embedded
into a sentence (cf. 4.2.1) or a sequence of sentences (cf. 4.2.2).
In other cases the third factor is extra-linguistic: the setting in
which the complex expression is used (cf. 4.2.3) or someone's
beliefs about what the expression means (cf. 4.2.4).

Such putative counterexamples are not all on the same level. Although
they all violate the letter of (C), some could be more easily
reconciled with productivity and systematicity than others. If it
turned out that in order to interpret an embedded sentence, one needs
information about the embedding sentence as well we would have to
conclude that the algorithm for calculating the meanings of complex
expressions is more complicated then we thought. But a complicated
algorithm is still an algorithm and the core explanation of how we
understand complex expressions would remain untouched. By contrast, if
it turned out that in order to interpret a sentence we must know all
sorts of ephemeral non-linguistic facts we would have to conclude that
the fact that we can reliably understand all sorts of unfamiliar
sentences is a mystery. Those who accept putative counterexamples of
this latter kind must provide alternative explanations for
productivity and systematicity.

(1) Everyone will succeed if he works hard.
(2) No one will succeed if he goofs off.

A good translation of (1) into a first-order language is (1′).
But the analogous translation of (2) would yield (2′), which is
inadequate. A good translation for (2) would be (2″) but it is
unclear why. We might convert ‘¬∃’ to the
equivalent ‘∀¬’ but then we must also
inexplicably push the negation into the consequent of the embedded
conditional.

This gives rise to a problem for the compositionality of English,
since is seems rather plausible that the syntactic structure of (1)
and (2) is the same and that ‘if’ contributes some sort of
conditional connective—not necessarily a material
conditional!—to the meaning of (1). But it seems that it cannot
contribute just that to the meaning of (2). More precisely, the
interpretation of an embedded conditional clause appears to be
sensitive to the nature of the quantifier in the embedding
sentence — a violation of
compositionality.[19]

One response might be to claim that ‘if’ does not
contribute a conditional connective to the meaning of either (1) or
(2) — rather, it marks a restriction on the domain of the
quantifier, as the paraphrases under (1″) and (2″)
suggest:[20]

(1″) Everyone who works hard will
succeed.
(2″) No one who goofs off will succeed.

But this simple proposal (however it may be implemented) runs into
trouble when it comes to quantifiers like ‘most’. Unlike
(3′), (3) says that those students (in the contextually given
domain) who succeed if they work hard are most of the students (in the
contextually relevant domain):

(3) Most students will succeed if they work hard.
(3′) Most students who work hard will succeed.

There are compositional proposals that handle this example, but the
obvious ones are ad hoc. Whether an elegant semantic analysis
can handle
if-clauses under quantifiers while obeying compositionality remains an
open question.[21]

(4) I dropped ten marbles and found all but one of them. It is
probably under the sofa.
(5) I dropped ten marbles and found nine of them. It is probably under
the sofa.

There is a clear difference between (4) and (5) — the first one is
unproblematic, the second markedly odd. This difference is plausibly a
matter of meaning, and so (4) and (5) cannot be synonyms.
Nonetheless, the first sentences are at least truth-conditionally
equivalent. If we adopt a conception of meaning where
truth-conditional equivalence is sufficient for synonymy, we have an
apparent counterexample to compositionality.

Few would insist that the first sentences of (4) and (5) are really
synonymous. What is interesting about this example is that even if we
conclude that we should opt for a more fine grained conception of
meaning, it is not immediately clear how that will account for the
contrast between these sentences. The difference is obviously due to
the fact that ‘one’ occurs in the first sentence of (4),
which is available as a proper antecedent for ‘it’ and
that there is nothing in the first sentence of (5) that could play a
similar role. Some authors have suggested that the right way to
approach this problem is to opt for a dynamic conception of meaning,
one that can encode anaphoric possibilities for subsequent
sentences.[22]

Interesting though these cases might be, it is not at all clear that
we are faced with a genuine challenge to compositionality, even if we
want to stick with the idea that meanings are just truth-conditions.
For it is not clear that (5) lacks the normal reading of (4) — on
reflection it seems better to say that the reading is available even
though it is considerably harder to get. (Contrast this with an
example due to — I think — Irene Heim: ‘They got
married. She is beautiful.’ This is like (5) because the first
sentence lacks an explicit antecedent for the pronoun in the
second. Nonetheless, it is clear that the bride is said to be
beautiful.) If the difference between (4) and (5) is only this, it is
no longer clear that we must accept the idea that they must differ in
meaning.

Suppose a Japanese maple leaf, turned brown, has been painted green.
Consider someone pointing at this leaf uttering (6):

(6) This leaf is green.

The utterance could be true on one occasion (say, when the speaker is
sorting leaves for decoration) and false on another (say, when the
speaker is trying to identify the species of tree the leaf belongs
to). The meanings of the words are the same on both occasions and so
is their syntactic composition. But the meaning of (6) on these two
occasions — what (6) says when uttered in these
occasions — is different. As Charles Travis, the inventor of this
example puts it: “…words may have all the stipulated
features while saying something true, but also while saying something
false.”[23]

At least three responses offer themselves. One is to deny the
relevant intuition. Perhaps the leaf really is green if it is painted
green and (6) is uttered truly in both situations. Nonetheless, we
might be sometimes reluctant to make such a true utterance for fear of
being misleading. We might be taken to falsely suggest that the leaf
is green under the paint or that it is not painted at
all.[24]
The second option is to point out that the fact that a
sentence can say one thing on one occasion and something else on
another is not in conflict with its meaning remaining the same. Do we
have then a challenge to compositionality of reference, or perhaps to
compositionality of content? Not clear, for the reference or content
of ‘green’ may also change between the two
situations. This could happen, for example, if the lexical
representation of this word contains an indexical
element.[25]
If this seems ad hoc, we can say instead that although there
is no context-dependent expression in (6) it can still be used to make
both true and false assertions. Perhaps the compositionally determined
occasion meanings are impoverished (perhaps not even propositional),
which is why they tend to be different from what speakers
assert.[26]

Perhaps the most widely known objection to compositionality comes from
the observation that even if e and e′ are
synonyms, the truth-values of sentences where they occur embedded
within the clausal complement of a mental attitude verb may well
differ. So, despite the fact that ‘eye-doctor’ and
‘ophthalmologist’ are synonyms (7) may be true and (8)
false if Carla is ignorant of this fact:

So, we have a case of apparent violation of compositionality; cf.
Pelletier (1994).

There is a sizable literature on the semantics of
propositional attitude reports.
Some think that considerations like this show that there are no
genuine synonyms in natural languages. If so, compositionality (at
least the language-bound version) is of course vacuously true. Some
deny the intuition that (7) and (8) may differ in truth-conditions and
seek explanations for the contrary appearance in terms of
implicature.[27]
Some give up the letter of compositionality but still provide
recursive semantic
clauses.[28]
And some preserve compositionality by postulating a hidden indexical
associated with
‘believe’.[29]

Acknowledgments

I thank Tamar Szabó Gendler, Michael Glanzberg, Tamás
Mihálydeák, and Jason Stanley for their comments. I am
especially grateful to Daniel Rothschild for catching an error and for
suggesting the repair in the preliminary draft of section 2. The entry
relies at many places on Szabó, 2000a,. Traffic sign images
are from the
Manual of Traffic Signs, by
Richard C. Moeur.

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